In recent years, attention has been given to a photonic crystal which is a two-dimensional or three-dimensional structure whose dielectric constant is periodically changed. Here, the two-dimension or three-dimension is determined based on the number of directions having periodicity. If an electromagnetic wave enters a photonic crystal composed of a periodic structure of two types of dielectric materials to cause Bragg diffraction, two standing waves are generated. They are a high energy standing wave generated in a low dielectric constant region and a low energy standing wave generated in a high dielectric constant region. Because a wave having energy between energies of these two standing waves cannot exist, a photonic band gap appears in the photonic crystal. An electromagnetic wave in the range of energy (wave length) in the photonic band gap cannot pass through the photonic crystal. The photonic band gap mentioned herein refers to the above phenomenon considered the same as that of a band gap (forbidden band) of the energy level of crystal electrons.
If a defect disturbing periodicity is introduced into a crystal having a photonic band gap, light can exist only in this defective portion. Thus, if the crystal is fabricated so as to have a region with the defect confined within the crystal, an optical resonator can be obtained. If the crystal is fabricated with the defect linearized within the crystal, a waveguide can be obtained. For example, in the case of a two-dimensional photonic crystal, an electric field component can be classified into a TE wave (transverse electric wave) parallel to a plane of the periodic structure and a TM wave (transverse magnetic wave) perpendicular to the plane of the periodic structure. In general, ranges of frequencies ω of photonic band gaps corresponding to respective lights do not necessarily coincide. Therefore, if a frequency range in which photonic band gaps occur concurrently for both the TE wave and the TM wave exists, the photonic band gap may be called a complete band gap.
A relatively simple structure photonic crystal of two-dimensional structure in which a complete band gap exists is known. The photonic crystal has through-holes (air holes) arranged on triangular lattices in a dielectric material as disclosed in, for example, Japanese Patent Laid-Open No. 2001-272555. In this case, the broadest complete band gap is obtained when the radius (r/a) is 0.48 and the frequency (ωa/2πc) is about 0.5. A character r represents a radius of the hole, a represents a lattice constant, ω represents an angular frequency of light, and c represents a light velocity in vacuum.
In a conventional two-dimensional photonic crystal in which air holes are arranged in a triangular lattice form, the complete band gap is obtained when the diameter d of the hole (=2r) equals 0.95a. The thickness of a wall between holes at the thinnest portion is very small, that is 0.05a, i.e. 0.035 μm, and therefore it is difficult to fabricate a two-dimensional photonic crystal in which the complete band gap can be obtained.
The present invention has been made based on this technical problem, and its object is to provide a photonic crystal which is easily produced and has a two-dimensional periodic structure capable of having a complete band gap for the TE wave and the TM wave.